An implicit equation specifies a relation among variables without solving explicitly for one of them. An equation 
defines an implicit plane
curve when its solution set is locally one-dimensional. At a point 
of this solution
set, if 
is continuously differentiable
near 
and 
,
the implicit function theorem gives a
local continuously differentiable function 
.
Implicit Equation
See also
Equation, Implicit Function, Implicit Function Theorem, Implicitization, Plane CurveExplore with Wolfram|Alpha
References
Krantz, S. G. and Parks, H. R. The Implicit Function Theorem: History, Theory, and Applications. Boston, MA: Birkhäuser, 2003. https://doi.org/10.1007/978-1-4612-0059-8.Cite this as:
Weisstein, Eric W. "Implicit Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ImplicitEquation.html